Answer:
The optimal size of each production run is 180 pounds, and the total annual inventory cost is $832,825.
Explanation:
To determine the optimal size and total annual inventory cost, we need to consider the production capacity, demand, setup costs, and carrying costs.
Given:
Production capacity per day = 250 pounds
Demand per day = 180 pounds
Setup cost = $125
Carrying cost per pound per year = $12
First, let's calculate the optimal production size. We want to produce enough cheese to meet the demand without exceeding the production capacity.
Optimal production size per day = Minimum(Production capacity, Demand)
Optimal production size per day = Minimum(250 pounds, 180 pounds) = 180 pounds
Next, let's calculate the total annual inventory cost. This cost includes both the setup cost and the carrying cost.
Total annual inventory cost = (Setup cost * Number of setups per year) + (Carrying cost per pound * Optimal production size * Number of days in a year)
Number of setups per year = Number of production runs per year
Number of production runs per year = Total days in a year / Days per production run
Assuming a year has 365 days and each production run takes one day:
Number of production runs per year = 365 days / 1 day = 365 runs
Total annual inventory cost = ($125 * 365) + ($12 * 180 pounds * 365)
Total annual inventory cost = $45,625 + $787,200
Total annual inventory cost = $832,825